# Transferring monotonicity in weighted norm inequalities.

Collectanea Mathematica (2003)

- Volume: 54, Issue: 2, page 181-216
- ISSN: 0010-0757

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topSinnamon, Gord. "Transferring monotonicity in weighted norm inequalities.." Collectanea Mathematica 54.2 (2003): 181-216. <http://eudml.org/doc/43083>.

@article{Sinnamon2003,

abstract = {Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions and quasi-concave functions. Under weaker partial orders on non-negative functions, monotone envelopes are re-examined and the level function is recognized as a monotone envelope in two ways. Using the level function, monotonicity can be transferred from the kernel to the weight in inequalities restricted to a cone of monotone functions.},

author = {Sinnamon, Gord},

journal = {Collectanea Mathematica},

keywords = {Desigualdades; Espacios de funciones medibles; Monotonicidad; Funciones de peso; quasi-concave functions; monotonicity; weight; inequalities},

language = {eng},

number = {2},

pages = {181-216},

title = {Transferring monotonicity in weighted norm inequalities.},

url = {http://eudml.org/doc/43083},

volume = {54},

year = {2003},

}

TY - JOUR

AU - Sinnamon, Gord

TI - Transferring monotonicity in weighted norm inequalities.

JO - Collectanea Mathematica

PY - 2003

VL - 54

IS - 2

SP - 181

EP - 216

AB - Certain weighted norm inequalities for integral operators with non-negative, monotone kernels are shown to remain valid when the weight is replaced by a monotone majorant or minorant of the original weight. A similar result holds for operators with quasi-concave kernels. To prove these results a careful investigation of the functional properties of the monotone envelopes of a non-negative function is carried-out. Applications are made to function space embeddings of the cones of monotone functions and quasi-concave functions. Under weaker partial orders on non-negative functions, monotone envelopes are re-examined and the level function is recognized as a monotone envelope in two ways. Using the level function, monotonicity can be transferred from the kernel to the weight in inequalities restricted to a cone of monotone functions.

LA - eng

KW - Desigualdades; Espacios de funciones medibles; Monotonicidad; Funciones de peso; quasi-concave functions; monotonicity; weight; inequalities

UR - http://eudml.org/doc/43083

ER -

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